Radio Frequency Integrated Circuit Design - Webs

164 Radio Frequency Integrated Circuit Design
Z in = −j
�C� + j�Le + g m L e
C� + j�Lb (6.61)
Note that to be matched, the real part of the input impedance must be
equal to the source resistance R S so that
Therefore,
g m L e
C� = R S (6.62)
L e = R S C�
=
g m
R S
�T
(6.63)
Note that if the Miller effect is considered, the value of the capacitance will be
larger than C� , and therefore a larger inductor will be required to perform the
match.
Also, the imaginary part of the input impedance must equal zero. Therefore,
L b =
1
C�� 2 − R S C�
g m
(6.64)
Making use of the above analysis, as well as the discussions on noise so
far, the following method for simultaneously matching an LNA for power and
noise was created. It is outlined in the following steps.
1. Find the current density in the process that will provide the lowest
minimum NF, and set the current density in the transistor to be this
value regardless of the size of the device. The minimum NF for a
process can be found from device measurements, but for the circuit
designer it can be determined by the use of simulators such as HPADS
or SPICE.
2. Once the current density is known, then the length of the transistor
le (equivalently, transistor emitter area, since the width is constant)
should be chosen so that the real part of the optimum source impedance
for lowest noise figure is equal to 50�. The current must be adjusted
in this step to keep the current density at its optimal level determined
in step 1.
3. Size L e , the emitter degeneration inductor, such that the real part of
the input impedance is 50�. The use of inductive degeneration will
tend to increase the real part of the input impedance. Thus, as this